Abstract
This paper proposes a numerical method to obtain an approximation solution for the timefractional Schrodinger Equation (TFSE) based on a combination of the cubic trigonometric B-spline collocation method and the Crank-Nicolson scheme. The fractional derivative operator is described in the Caputo sense. The L-1-approximation method is used for time-fractional derivative discretization. Using Von Neumann stability analysis, the proposed technique is shown to be conditionally stable. Numerical examples are solved to verify the accuracy and effectiveness of this method. The error norms L-2 and L-infinity are also calculated at different values of N and t to evaluate the performance of the suggested method.